Pseudo-differential operators & Markov processes: 3 Markov processes and applications
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Imperial College Press
2005
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVIII, 474 S. |
| ISBN: | 1860945686 |
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MARC
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| 100 | 1 | |a Jacob, Niels |d 1955- |e Verfasser |0 (DE-588)141510129 |4 aut | |
| 245 | 1 | 0 | |a Pseudo-differential operators & Markov processes |n 3 |p Markov processes and applications |c N. Jacob |
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| 300 | |a XXVIII, 474 S. | ||
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| 650 | 4 | |a Potential theory (Mathematics) | |
| 650 | 4 | |a Pseudodifferential operators | |
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Record in the Search Index
| _version_ | 1804139934154489856 |
|---|---|
| adam_text | Contents
Preface
ix
Notation xi
General Notation............................. xi
Functions and Distributions
....................... xiii
Measures
and Integrals.......................... xiv
Spaces
of Functions, Measures and Distributions
........... xiv
Some Families of Functions
....................... xvi
Norms, Scalar Products and Seminorms
................ xvii
Notation from Functional Analysis, Operators
............. xvii
Notations related to Pseudo-Differential Operators
.......... xix
Notations related to Potential Theory and Harmonic Analysis
.... xix
Notation from Probability Theory
................... xx
Stochastic Processes and related Notations
.............. xxi
Notations related to
càdlàg-Functions
................. xxii
Notations related to Hunt Processes and I,p-Markovian Semigroups
. xxiii
Some more Special Notations
...................... xxiii
Introduction: Pseudo-Differential Operators and Markov
Processes
xxv
III Markov Processes and Applications
1
1
Introduction
3
2
Essentials from Probability Theory
9
2.1
Some Remarks on
σ
-Fields
and Measures
............ 9
Contents
2.2
Some
Integration
Theory
..................... 17
2.3
Measure and Topology
....................... 22
2.4
Independence
............................ 24
2.5
Conditional Expectation
...................... 27
2.6
Martingales and Stopping Times
................. 33
2.7
Some Remarks to Stochastic Processes
.............. 41
Feller Processes
45
3.1
Projective
Limits and Canonical Processes
............ 46
3.2
Semigroups of Kernels, Transition Functions and Canonical Pro¬
cesses
................................ 51
3.3
A First Encounter with Sample Paths and
Càdlàg-Functions
. . 71
3.4
Markov Processes and Feller Processes
.............. 80
3.5
The Shift Operator and the Strong Markov Property
...... 96
3.6
The Martingale Problem for Feller Processes
.......... 108
3.7
Levy Processes and Translation Invariant Feller Semigroups
. . 115
3.8
A Summary of Some Path Properties of Levy Processes
.... 141
3.9
The Symbol of a Feller Process
.................. 146
3.10
Notes to Chapter
3......................... 152
The Martingale Problem
157
4.1
Probability Measures on
©„([0,
co))
............... 158
4.2
Existence Results for the Pn-Martingale Problem
........ 174
4.3
A Uniqueness Criterion for the Solvability of the Martingale
Problem
............................... 191
4.4
A Localization Procedure
..................... 198
4.5
On the Well-Posedness of the Martingale Problem
....... 201
4.6
The Martingale Problem and the Feller Property
........ 214
4.7
Notes to Chapter
4......................... 221
jC-sub-Markovian Semigroups and Hunt Processes
223
5.1
Why the Theory of Feller Processes is not Sufficient
...... 223
5.2
Hunt Processes
........................... 227
5.3
Hunt Processes Associated with Lp-sub-Markovian Semigroups
252
5.4
Markov Processes Associated with an ¿p-sub-Markovian Semi¬
group
................................ 276
5.5
Notes to Chapter
5......................... 279
Contents
vii
6
Markov Processes and Potential Theory
283
6.1
Heuristic Links between Markov Processes and Potential Theory
284
6.2
Potential Theoretical Notions and their Probabilistic Counterparts
287
6.3
Potential Theory of Levy Processes and more Probabilistic
Counterparts
............................310
6.4
Applications to Markov Processes
.................319
6.5
The Balayage-Dirichiet Problem
.................329
6.6
Notes to Chapter
6.........................351
7
Selected Applications and Extensions
353
7.1
Fractional Derivatives as Generators of Markov Processes
. . . 354
7.2
Remarks on Markov Processes with State Spaces Having a
Boundary
.............................. 368
7.3
Making Parameters State Space Dependent
........... 385
7.4
Remarks on Stochastic Spectral Analysis
............. 389
7.5
Function Spaces Associated with a Continuous Negative Definite
Function
............................... 393
7.6
Notes to Chapter
7......................... 400
A Parametrix Construction for Evolution Equations
403
8
A Parameter Dependent Extension of Hoh s Calculus
407
С
On Roth s Method for Constructing Feller Semigroups
411
D
More Continuous Negative Definite Functions
415
E More
(Complete) Bernstein Functions
419
Corrections to Volume I
422
Corrections to Volume II
423
Changes in the Bibliography of Volume II
424
Bibliography
425
Author Index
457
Subject Index
463
|
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| id | DE-604.BV035722419 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:51:58Z |
| institution | BVB |
| isbn | 1860945686 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017999173 |
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| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-384 |
| physical | XXVIII, 474 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Jacob, Niels 1955- Verfasser (DE-588)141510129 aut Pseudo-differential operators & Markov processes 3 Markov processes and applications N. Jacob London Imperial College Press 2005 XXVIII, 474 S. txt rdacontent n rdamedia nc rdacarrier Markov processes Potential theory (Mathematics) Pseudodifferential operators (DE-604)BV014229605 3 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017999173&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jacob, Niels 1955- Pseudo-differential operators & Markov processes Markov processes Potential theory (Mathematics) Pseudodifferential operators |
| title | Pseudo-differential operators & Markov processes |
| title_auth | Pseudo-differential operators & Markov processes |
| title_exact_search | Pseudo-differential operators & Markov processes |
| title_full | Pseudo-differential operators & Markov processes 3 Markov processes and applications N. Jacob |
| title_fullStr | Pseudo-differential operators & Markov processes 3 Markov processes and applications N. Jacob |
| title_full_unstemmed | Pseudo-differential operators & Markov processes 3 Markov processes and applications N. Jacob |
| title_short | Pseudo-differential operators & Markov processes |
| title_sort | pseudo differential operators markov processes markov processes and applications |
| topic | Markov processes Potential theory (Mathematics) Pseudodifferential operators |
| topic_facet | Markov processes Potential theory (Mathematics) Pseudodifferential operators |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017999173&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014229605 |
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